> On 6 Feb., 04:47, Ralf Bader <ba...@nefkom.net> wrote:>> According to Mückenheim, "There is no>> sensible way of saying that 0.111... is more than every>> FIS". Of the authorities you called upon, whom would you find capable of>> regardng this as a sensible assertion>> Compare Matheology § 030: We can create in mathematics nothing but> finite sequences, and further, on the ground of the clearly conceived> "and so on", the order type omega, but only consisting of equal> elements {{i.e. numbers like 0,999...}}, so that we can never imagine> the arbitrary infinite binary fractions as finished {{Brouwers Thesis,> p. 143}}. [Dirk van Dalen: "Mystic, Geometer, and Intuitionist: The> Life of L.E.J. Brouwer", Oxford University Press (2002)]

"Where one says 'and so on', one means the arbitrary repetition of the same thing or operation, even though that thing or operation may be defined in a complex way"

thus justifying existence of expansions like 0.12121212...

"arbitrary" sequences are a different matter.

And in van Dalen, p 118, a letter from Brouwer summarising his thesis: "I can formulate: 1. Actual infinite sets can be created mathematically, even though in the practical applications of mathematics in the world only finite sets exist."